When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves

Buchanan, Robert L.; Whiting, Richard C.; Damert, W.C

doi:10.1006/fmic.1997.0125

Cited by 446 publications

(277 citation statements)

References 18 publications

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“…1A). We consider a minimal three-phase model of growth dynamics in which the growth curve is characterized by three quantitative traits, one corresponding to each phase of growth [25,26]: a lag time λ, an exponential growth rate g, and a saturation population size N sat (Fig. 1A, Sec.…”

Section: Methodsmentioning

confidence: 99%

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection

Manhart¹,

Adkar²,

Shakhnovich³

2018

Proc. R. Soc. B.

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Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple life-history traits to selection is a critical question for evolutionary biology as we seek to predict the evolutionary fates of mutations. Here we use a model of microbial growth to show there are two distinct components of selection corresponding to the growth and lag phases, while the yield modulates their relative importance. The model predicts rich population dynamics when there are tradeoffs between phases: multiple strains can coexist or exhibit bistability due to frequency-dependent selection, and strains can engage in rock-paperscissors interactions due to non-transitive selection. We characterize the environmental conditions and patterns of traits necessary to realize these phenomena, which we show to be readily accessible to experiments. Our results provide a theoretical framework for analyzing high-throughput measurements of microbial growth traits, especially interpreting the pleiotropy and correlations between traits across mutants. This work also highlights the need for more comprehensive measurements of selection in simple microbial systems, where the concept of an ordinary fitness landscape breaks down.

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Section: Methodsmentioning

confidence: 99%

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection

Manhart¹,

Adkar²,

Shakhnovich³

2018

Proc. R. Soc. B.

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“…Many growth models have thus been developed. Among them, a modified Gompertz model, the three-phase linear model, and especially the Baranyi model are well-known Gibson et al, 1987;Baranyi and Roberts, 1994;Buchanan et al, 1997 . We also developed an extended logistic model, which is called the new logistic NL model Fujikawa et al, 2003 andFujikawa and Morozumi, 2005 . The NL model is described as below.…”

Section: Introductionmentioning

confidence: 99%

Development of a Competition Model for Microbial Growth in Mixed Culture

2014

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A novel competition model for describing bacterial growth in mixed culture was developed in this study. Several model candidates were made with our logistic growth model that precisely describes the growth of a monoculture of bacteria. These candidates were then evaluated for the usefulness in describing growth of two competing species in mixed culture using Staphylococcus aureus, Escherichia coli, and Salmonella. Bacterial cells of two species grew at initial doses of 10 Biocontrol Science, 2014, Vol. 19, No. 2, 61 71 Here N is the microbial population at time t. N max and N min correspond to the maximum and the initial cell populations, respectively. m and n are the parameters for the curvature of the deceleration phase and the period of the lag phase, respectively Fujikawa, 2010 .The NL model has been shown to describe and predict microbial growth in broth and on agar plates successfully at constant and dynamic temperatures Fujikawa et al., 2003 andFujikawa and Morozumi, 2005 . It could further predict the amount of s t a p h y l o c o c c a l e n t e r o t o x i n A p r o d u c e d b y Staphylococcus aureus in milk and a blue pigment caused by Pantoea agglomerans on agar plate Fujikawa and Morozumi, 2006;Fujikawa and Akimoto, 2011 . We now consider the NL model to be a

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“…A biphasic linear model (Buchanan et al 1997) was fitted to the SEC concentration produced at a particular log bacterial number. The model was fitted using the Solver routine in Excel (Microsoft, WA, USA).…”

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confidence: 99%

Modelling production of S. aureus enterotoxin Cbovine in milk, and its production during cheesemaking

Hunt

Butler

Jordan

2015

Dairy Sci. & Technol.

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Staphylococcal enterotoxin type C (SEC) is one of the classical enterotoxins implicated in staphylococcal food poisoning. Staphylococcus aureus strains isolated from bovine unpasteurised milk and associated cheese samples produced the SEC bovine sub-type. The objectives of this study were to determine the cell numbers required for SEC bovine production in milk and to determine if SEC bovine was produced by S. aureus during cheesemaking. To predict the point at which toxin production begins, SEC production was modelled against cell numbers of S. aureus (at different controlled pH/ temperature combinations) in sterile reconstituted milk using a biphasic model fitted using the Solver routine in Excel. Under the conditions tested, the average cell number required for SEC bovine production was log 8.43±0.39 in sterile reconstituted milk. A semi-soft cheese was manufactured using milk inoculated with either washed (to remove any pre-formed toxin) or unwashed (containing toxin) S. aureus at 10 5 and 10 7 cfu.mL −1. An enzyme-linked immunosorbent assay was used to quantify toxin production and Baird-Parker agar to quantify S. aureus. Cheese made with washed and unwashed cells showed a one log increase in S. aureus cell numbers during cheesemaking. In cheese made with washed cells, no SEC was detected. With unwashed cells, the SEC concentration remained constant throughout cheesemaking. The , and therefore, the risk-associated with SEC bovine in cheese is low.Dairy Sci. & Technol. (2015) 95:747-757 DOI 10.1007/s13594-015-0228-3 This paper is

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When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves

Cited by 446 publications

References 18 publications

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection

Trade-offs between microbial growth phases lead to frequency-dependent and non-transitive selection

Development of a Competition Model for Microbial Growth in Mixed Culture

Modelling production of S. aureus enterotoxin Cbovine in milk, and its production during cheesemaking

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